Are there any other obvious accident in a water cooled reactor that can challenge the containment?
I can't really think of any beyond seismic loadings and LOCAs/SBO accidents.
We also have a response to a Loss of Ultimate Heat Sink accident - since all the emergency cooling systems evaporate water into the atmosphere directly.

I wonder, if the entire shield wall is constructed of steel plate formed concrete, whether we could have the annulus and containment vessel arrive in sections, attached to the shield building walls. It would reduce the number of field welds since the segments would only have to be joined up to make the final shape.

In other words, the shield building and containment vessel would arrive as segments, with the containment vessel segment fixed to the shield wall by an annulus plate.
Horizontal welds are easier to do than vertical ones over large distances (since a worker can do the whole weld in one go on a catwalk) and thus we would want to have only say eight segments around the containment, with each one being relatively short to keep its weight within reason.

Careful arrangement of the steam lines, feedwater lines and the like would also allow 6 of these segments to be identical as they would have no wall penetrations and one of the last two only have an alternative feedwater intake pipe from the annulus [all the steam lines and the like would go out through the last segment, directly to the turbine hall, and would likely have the main airlocks.]

In my opinion the most serious challenge to containment for LWRs are containment bypass events combined with core damage. They defeat both containment and the pccs (as this needs pressure to function in terms of condensation with a 100C passive heat sink). They're low probability though, with good valve design, etc. as in the ap1000. BWRs need to think about shutdown risk releases though.

Loss of heat sink type is lower consequence but far higher probability. This is the key design area focus in my opinion. LOHS, SBO, LOFC, those kind of accidents. Having a moat of water in place at all times is a robust way of dealing with these accidents. Very similar to NuScale.

I am struggling to work out what is actually using the huge ~65,000m3 internal volume of the containment vessel.

Since I am proposing a HWR reactor I am even pondering putting the detritiation plant (which also acts as an upgrader) in there, as long as I can keep the hydrogen gas inventory down to a few grammes.

Does the AP1000 allow access to (parts of) the containment on power?
I know certain reactors do, for example the CANDU 6 family (not Bruce/Darlington though!) and am wondering about the AP1000. This also is relevant as they have to be able to escape if a LOCA occurs whilst they are working in the containment, and thus the pressure/temperature rise must be kept fairly slow at least for the first minute or so of the accident. This is not a huge problem with a prestressed vessel but I imagine it could be with a traditional steel one.

Yeah it is mostly empty space. Need it for steam expansion. Steam is 3 orders of magnitude more volume than water. So lots of volume needed. Why pressure suppression is so clever. Just need to get rid of those pesky non condensables... SiC cladding to the rescue.

There are several contradicting issues. The volume must contain both the steam and the steam heated air. The volume vessel must be structurally sound under a wide variety of loads. The volume vessel must be thin enough in proportion to its area to pass the decay heat.

SiC cladding would be helpful because it would enable the removal (if we can also get all the core hardware that is ZIrconium converted to) of most of the recombiners and such.
But that is a bit much to hope for, but I think most of the effort has to be concentrated on avoiding core damage in the first place.

At least if the containment vessel is breached in this design it is likely to lead to the annulus pool draining into the reactor containment, which at least keeps its covered for a long time.

Primary Loop: ~100 bar, 309C outlet 10% quality
PCHE type Moderator coolers will heat the feedwater to ~280C or so, and if we accept only ~10C subcooling in the primary loop almost all the energy would be transferred in the steam generators by condensation/boiling, that has very high heat transfer coefficients.

If we use helical once-through steam generators (biiiig ones) then we can get a lot of heat generator area into a relatively compact package, and the higher heat transfer coefficient will allow us to squeeze the delta-T.

My current projection is 80 bar steam at 305C (Ocobee Unit 1 has an outlet delta-T of only ~3C apparently), which is roughly 15C of superheat.